package com.wc.AlgoOJ_homework.AlgoOJ_HomeWork2.I_等差数列;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

/**
 * @Author congge
 * @Date 2024/3/5 23:04
 * @description http://43.138.190.70:8888/p/LQ1007?tid=65e6b15c27489dab814f8d41
 */
public class Main {
    static FastReader sc = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);
    static int N = 100010;
    static int[] a = new int[N];
    static int n;

    public static void main(String[] args) {
        n = sc.nextInt();
        for (int i = 1; i <= n; i++) a[i] = sc.nextInt();
        Arrays.sort(a, 1, n + 1);
        if (a[1] == a[n]) {
            System.out.println(n);
            return;
        }
        int d = a[2] - a[1];
        for (int i = 2; i <= n; i++) d = gcd(d, a[i] - a[i - 1]);
        int res = (a[n] - a[1]) / d + 1;
        out.println(res);
        out.flush();
    }

    static int gcd(int a, int b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }
}

class FastReader {
    StringTokenizer st;
    BufferedReader br;

    FastReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    String nextLine() {
        String s = "";
        try {
            s = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return s;
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    double nextDouble() {
        return Double.parseDouble(next());
    }

    // 是否由下一个
    boolean hasNext() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                String line = br.readLine();
                if (line == null)
                    return false;
                st = new StringTokenizer(line);
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return true;
    }
}